Question 3 (i)
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?
43.123456789

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Solution

Since this number has a terminating decimal expansion, it is a rational number of the form $\frac{p}{q}$ .
And, q is of the form $2^{m} \times 5^{n}$ where n and m are non-negative integers.

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Question 3 (i) The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form pq, what can you say about the prime factors of q? 43.123456789

Since this number has a terminating decimal expansion, it is a rational number of the form pq. And, q is of the form 2m× 5n where n and m are non-negative integers.

Question 3 (i)
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?
43.123456789

Since this number has a terminating decimal expansion, it is a rational number of the form $\frac{p}{q}$ .
And, q is of the form $2^{m} \times 5^{n}$ where n and m are non-negative integers.